Translation:Does she think they believed or not?
without a personal subject pronoun, the sentence sounds weird
Having said that, yes, the sentence with the subjunctive in my opinion sounds better
passato remoto "Lei pensa che (mi, ci, vi,...) credettero?"
congiuntivo passato "Lei pensa che (mi, ci, vi,...) abbiano creduto?"
I am getting a bit out of my depth, but I would say that you would normally use subjunctive with "pensa che" where there was room for doubt and the person in the main clause differs from the person in the dependent clause. However there is no subjunctive mood with passato remoto (credettero) so you could just leave it as it is or change to congiuntivo passato if you were talking about a distinct completed action. I should have thought that with "credere" the imperfetto might be a better tense anyway (depending on the context) and that that would allow use of the congiuntivo imperfetto. Perhaps a native speaker can tell us what the best way to say this is.
So, I'm looking for the pronoun "it" in this sentence. It seems almost unforgivable everywhere else to be without it. The Italians say "Lo so," implying the subject "I" but including the object "it..." We, in English, would say "I know," not necessarily "I know it." There might be an English usage where we would say, "Does he believe." But in my experience thus far with Italian, they would be immediately asking me, "Does he believe what?" except in the above example, apparently... A native Italian speaking friend told me that their are grammatical rules in Italian, and rules are rules... until they're not...